Diagnostics of Coronal Heating in Active-Region Loops

Abstract

Understanding coronal heating remains a central problem in solar physics. Many mechanisms have been proposed to explain how energy is transferred to and deposited in the corona. We summarise past observational studies that attempted to identify the heating mechanism and point out the difficulties in reproducing the observations of the solar corona from the heating models. The aim of this paper is to study whether the observed EUV emission in individual coronal loops in solar active regions can provide constraints on the volumetric heating function, and to develop a diagnostics for the heating function for a subset of loops that are found close to static thermal equilibrium. We reconstruct the coronal magnetic field from SDO/HMI data using a non-linear force free magnetic field model. We model selected loops using a 1D stationary model, with a heating rate dependent locally on the magnetic field strength along the loop, and calculate the emission from these loops in various EUV wavelengths for different heating rates. We present a method to measure a power index β defining the dependence of the volumetric heating rate E H on the magnetic field, E H ∝ B β , and controlling also the shape of the heating function: concentrated near the loop top, uniform and concentrated near the footpoints. The diagnostics is based on the dependence of the electron density on the index β. This method is free from the assumptions of the loop filling factor but requires spectroscopic measurements of the density-sensitive lines. The range of applicability for loops of different length and heating distributions is discussed, and the steps to solving the coronal heating problem are outlined.

The Relation Between Magnetic Fields and X-ray Emission for Solar Microflares and Active Regions

“…Thus, our results demonstrate that there should be two different heating mechanisms in pre-flaring active regions and during the microflares: Alfvén wave heating for active regions, and magnetic reconnection for microflares. The evidence supporting the presence of Alfvén wave turbulence heating in active regions has been presented by Fludra, Hornsey, and Nakariakov (2017).…”

The Heating of Solar Coronal Loops by Alfvén Wave Turbulence

“…Many coronal loops seen in EUV and X-ray images have nearly constant cross-sections (e.g., Klimchuk 2000;López-Fuentes et al 2006, 2008, which appears to be in conflict with the basic idea that the magnetic field lines expand with height in the corona. Observations of the "moss" at the ends of hot loops provide constraints on the energy losses by downward conduction (Fletcher & de Pontieu 1999;Martens et al 2000;Warren et al 2008;Winebarger et al 2011), and measurements of plasma density can provide constraints on the spatial distribution of the heating (Fludra et al 2017). Second, the model should reproduce the observed spectral line widths, which are broadened in excess of their thermal widths (e.g., Doschek et al 2007;Young et al 2007;Tripathi et al 2009;Warren et al 2011;Tripathi et al 2011;Tian et al 2011Tian et al , 2012aDoschek 2012;Brooks & Warren 2016;Testa et al 2016).…”

The Properties of the Solar Corona and Its Connection to the Solar Wind

“…With the advent of efficient computers, it has become possible to perform large-scale pixel-bypixel comparisons between observed coronal images and synthesized trial images created with a range of guesses about the heating rate. Different dependences of Q on quantities such as the coronal field strength B and the loop length L produce very different patterns of synthetic EUV and X-ray emission (Mandrini et al 2000;Schrijver et al 2004;Lundquist et al 2008;Fludra et al 2017). For example, Schrijver et al (2004) found a best fit with observations for Q ∝ B/L 2 , which is roughly equivalent to E ≈ Λ 2 Θ, or the prediction from the Parker (1983) braiding model.…”